Question

Mary and Jane went on a tour together. Mary brought twice as much money as Jane. After Mary had spent $800 and Jane had spent $240, they had equal amount of money left. How much money did Mary have at first?

Answer 1

Mary had $1,120

Explanation:

Let the amount mary and jane had be 2x and x respectively.

Let the equal amount be y:

`mary \: (y = 2x - 800) \\ jane \: (y = x - 240)`

Using the simultaneous equation method, multiply the first equation by the coefficient of x(1) of the second equation and the second equation by the coefficient of x(2) of the first equation:

`y = 2x - 800 \\ 2y = 2x - 480`

Subtract the second equation from the first equation:

`- y = - 320 \\ y = 320`

$320 was their equal amount.

Substitute 320 for y in any equation:

`y = x - 240 \\ 320 = x - 240 \\ x = 320 + 240 \\ x = 560 \\ \\ 2x = 1120`

Therefore, Jane had $560 at first and Mary had $1120 at first.

Answer 2

Mary has $1120

Explanation:

money mary has at first : x

money jane has at first : y

Mary brought twice as much money as Jane : x=2y

Mary had spent $800 and Jane had spent $240, they had equal amount of money left : x-800=y-240

=>
`\left \{ {{x=2y} \atop {x-800=y-240}} \right.`

=> x=1120

y=560